Math Forum / Mathematics / Algebra Help / June 2008

I told my brother who is doing math by correspondence that I would help him
with his math homework, but now I'm stuck with this problem.
We've spent several hours now and have got our guts wound into knots with
anxiety. Well , here's hoping ...

So here is the question I am supposed to answer:
If two sides and the angle opposite one of them in a triangle are
equal to the corresponding parts of another triangle, then it follows
that the triangles are congruent.

I am reviewing statistics and probabilty and have a somewhat off-
tangent question:
I understand that variance and standard deviation relate the question
of how 'spread out' a data set is from the mean.  In general, the

In the CliffsTestPrep book for the California CSET, the following
problem (and siglum) is mentioned:
If R and S are integers, then R | S if and only if R^2 | S^2.
and

James Stewart, in ``Calculus'' (5th edition, at least) mentions that if
the root test yeilds 1, then the ratio test will yeild 1 as well. This
makes me think that the root test is stronger. I haven't found a proof
of this on the web. I'd like to see one. Any books or URLs? Thank you ...

I am busy with the book "Lineair Algebra demystified"
It states "if matrix A and B both have inverses, then their sum (A+B) also
has an inverse (A+B)^-1 " But no proof is given. How to prove it ?
Anybody knows ?

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Hoping for how to find the formula...
This is actually Geometry.
Hoping you might help
If two sides of a square field were increased by five feet the area of the

In the discussion of the equation
y = f(x) = 2 * sqrt(9 - x^2)
(2 times the square root of {9 - x squared}),
the author writes the following:

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Is there available simple & free software
that can be used to prepare math-related
documents under Windows?
Something like the LaTex software?

In one of my CSET test prep books, the following problem is posed:
Let a, b represent positive integers less than 19 for which 19 = a
(mod 3) and 27 = b (mod 4).  What is the maximum value of a - b?
The equal sign used here stands for a three-lined equal sign in the

One of the problems in Schaum's review of linear algebra shows how a
2x2 matrix can be the input element of a function f(x), and that if
that results in a 2x2 zero matrix, the initial 2x2 matrix is a root of
the f(x).

I understand that matrix multiplation is not commutative (that is,
order matters in most cases).  So if I have a matrix A such as:
[ a    b ]
[ c    d ]

A friend's daughter is in the first year of high-school, and she is
severely bored by the mathematics class.  Last year she did a fair bit
of extension work, so she has already seen most of what is being covered
this year.  I figure that further extension work for her would just